Basic Examples (2) 

Determine all shortest paths on a random graph:

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Verify that the output above is indeed Directed and Acyclic:

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Scope (3) 

Explore traversal maps of a Petersen graph:

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Add another Graph-exploring reference point and compare possible pairwise dance moves:

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Check to see that edges are lost only on odd cycles:

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Compare what happens when different initial conditions are chosen:

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Options (2) 

Acyclic directed graphs can be plotted as causal graphs by setting VertexCoordinates to Automatic:

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Plot a few more causal graphs:

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Properties and Relations (1) 

The transformation acts as the identity on rows of the GraphDistanceMatrix:

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Possible Issues (2) 

Specifying multiple reference points can divide the graph into disconnected components:

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The function will balk at nonsense inputs:

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Neat Examples (5) 

Count possible walks on all Petersen graph outputs:

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List a sequence that does not have an entry in the OEIS:

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Plot the possibly new sequence:

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Conjecture the form of a linear recurrence:

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Compare with depictions to try and formulate a proof argument:

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